As for image data of a pathological specimen (virtual slides), not only horizontal information of the specimen but also its information in the optical axis direction of an imaging optical system (hereinafter the “optical axis direction” for short) is an important material for pathological diagnosis. Accordingly, a conventional method for a microscope changes the focus position in the optical axis direction of the imaging optical system, thereby acquiring a plurality of images (Z-stack images) of the specimen.
In order to observe in detail the specimen structure in the optical axis direction, space intervals at which the focus position is changed when acquiring Z-stack images, need to be small enough. Hereinafter, unless otherwise specified, Z-stack images are acquired with different focus positions at equal space intervals, and the interval is called a “focusing step”. The sampling theorem is known as a standard to determine the focus step. When this is applied to the acquisition of Z-stack images, the inverse of the focus step needs to be twice or more the maximum value of the spatial frequency in the optical axis direction that a three-dimensional optical image has (the Nyquist condition). Hereinafter, only the focus step (the sampling interval in the optical axis direction) is subject to the Nyquist condition, and for horizontal directions, which are perpendicular to the optical axis direction, the Nyquist condition is disregarded. The spatial frequency of the optical image is a frequency range in which the spectrum has a non-zero value obtained by performing a discrete Fourier transform for the intensity distribution data of the optical image. If the focusing step is determined according to the Nyquist condition, the focusing step will be a relatively small value on the order of the wavelength of the illumination light, so that the data volume of Z-stack images is enormous. This method results in an increase in the cost of hardware related to the acquisition, processing, and storing of images and an increase in processing time.
Subjected to the resolving power defined by the optical system of the microscope, acquired images of a specimen are degraded relative to the actual specimen. In order to restore these degraded images, PLT1 restores an image by image processing without considering the sparseness of a specimen, but the resolution of acquired Z-stack images and the resolution of restored images are the same. As a time period required to acquire Z-stack images is shortened with a larger focusing step, the resolution in the optical axis direction of the specimen degrades accordingly. Further, if the Nyquist condition is not satisfied, aliasing (fold distortion) occurs, resulting in the occurrence of a false pattern in the structure in the optical axis direction in Z-stack images. One solution for this problem is the interpolation that increases the resolution in the optical axis direction of the Z-stack images, but according to the sampling theorem, the correctness of interpolation is not ensured when the Nyquist condition is not satisfied.
Accordingly, there has been growing interest in a novel signal processing technique referred to as compressed sensing or compressive sensing in these years. The compressive sensing is a technique which accurately reconstructs information about an object subject to observation from data sampled without the Nyquist condition being satisfied.
For example, NPLT1 discloses a method of reconstructing three-dimensional shape information of a specimen from one image by applying the compressive sensing to a hologram. PLT2 discloses a method which, with an improvement in the optical element or image pickup element, generates an image from which the amount of information obtained is not essentially reduced even when the sampling interval is increased, to reconstruct an image higher in resolution than an acquired image (a super-resolution process). PLT3 discloses a method of optimizing an objective function including a noise suppression term and a sparse regularization term in a tomographic image acquiring apparatus such as an MRI (Magnetic Resonance Imaging) for the image reconstruction. This method uses a regularization with the sparseness of a solution as prior information, and provides a highly accurately reconstruction with a reduced number of acquired data if the three-dimensional information of a specimen is sparse (the number of non-zero elements is small).
NPLT2 describes imaging by a microscope, and NPLT3 describes the accuracy of reconstruction in the compressive sensing. NPLT4 describes a TwIST algorithm, and NPLT5 describes a weak-object optical transfer function.